To relate this moduli space to the quantum gauge theory defined in
Section REF , we note that the weak-coupling limit \(e\longrightarrow 0\)  of
the Yang-Mills action functional (REF ) is either 0 or it diverges to \(+\infty \) , and hence the path integral (REF )
localizes onto gauge field configurations with vanishing action
functional, or equivalently with vanishing curvature \(F_A=0\) ; these
are precisely the flat
twisted bundles. Hence the path integral formally reduces to an integral
over \({M}_G^D(\Sigma )\) .
Since the integration measure
\({D}(P,A)\)  is formally induced by the
infinite-dimensional symplectic structure (REF ), it is natural to conjecture that
the partition function (REF ) computes the symplectic volume of
\({M}_G^D(\Sigma )\)  in the weak-coupling limit, where the symplectic
two-form on \({M}_G^D(\Sigma )\)  is inherited from (REF ). This argument is
completely analogous to that given in the case of ordinary Yang-Mills
theory in [1]}.
